We assume that distributional shifts are bounded at each time point.
Similar smoothness assumptions have been advocated in previous works [1]} as a more realistic representation of real-world problem settings.
We formalize this assumption in terms of the maximum mean discrepancy (MMD), a distance-measure between probability measures [2]}.
For any two distributions \(Q_1, Q_2 \in \mathcal {P}\) , define the MMD with respect to the function class \(\lbrace (x, y) \mapsto \ell (\tilde{g}(x), y) : \tilde{g} \in \mathcal {G} \rbrace \)  as
\(\operatorname{MMD}(Q_1, Q_2):=\sup _{\tilde{g} \in \mathcal {G}}\left|\operatorname{\mathbb {E}}_{Q_1} \ell (\tilde{g}(X), Y) - \operatorname{\mathbb {E}}_{Q_2} \ell (\tilde{g}(X), Y)\right|.\) 
